Summary
A GMRES solver based on the estimation of the gradient of the objective function gradient algorithm are used for the reconstruction and optimization of airfoils represented by cubic splines and operating at subsonic and transonic conditions. It is shown that the number of iterations has been multiplied by three between the subsonic and the transonic case. For the optimization problem, the drag objective function is penalized to take into account the lift constraint. Two descent methods, namely a fixed step gradient and a conjugate gradient algorithm are investigated. Results are compared with a GMRES optimizer for the solution of the optimality conditions using the calculus of variations with adjoint equations. These methods have been developped in close cooperation with O. Pironneau and A. Vossinis at INRIA Rocquencourt.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Cea. Conception optimale ou identification de formes: calcul rapide de la dériv’ee directionnelle de la fonction coût. Notes de cours à l’Université de Nice.
F. Angrand. Thèse Seme cycle. Université Paris VI.
Q.V. Dinh and J.W. He. A Cartesian Grid Finite Element Method for Potential Flows. 2nd Symposium on High Performance Computing, October 7–9, 1991, Montpellier, France.
P.N. Brown and Y. Saad. Globally convergent techniques in nonlinear Newton-Krylov algorithms. Technical Report 89-57, Research Institute for Advanced Computer Science, 1989.
P.N. Brown and Y. Saad. Hybrid Krylov methods for nonlinear systems of equations. SIAM J. Sci. Stat. Comp., 27, 1990.
O. Pironneau and A. Vossinis. Comparison of some optimization algorithms for optimum shape design in aerodynamics. INRIA Report, 1991.
D. Joannas, B. Mantel, J. Periaux and B. Stoufflet. 12 month report BRITE/EURAM Optimum Design.
Q.V. Dinh, D. Joannas, J.W. He, B. Mantel, J. Periaux and B. Stoufflet. 18 month report BRITE/EURAM Optimum Design.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
About this chapter
Cite this chapter
Dinh, Q.V., Mantel, B., Periaux, J., Stoufflet, B. (1997). Contribution to Problems T4 and T6 Finite Element GMRES and Conjugate Gradient Solvers. In: Periaux, J., Bugeda, G., Chaviaropoulos, P.K., Labrujere, T., Stoufflet, B. (eds) EUROPT — A European Initiative on Optimum Design Methods in Aerodynamics. Notes on Numerical Fluid Mechanics (NNFM), vol 55. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-86570-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-322-86570-0_3
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-322-86572-4
Online ISBN: 978-3-322-86570-0
eBook Packages: Springer Book Archive